4x^2+26x-25=0

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Solution for 4x^2+26x-25=0 equation:


Simplifying
4x2 + 26x + -25 = 0

Reorder the terms:
-25 + 26x + 4x2 = 0

Solving
-25 + 26x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-6.25 + 6.5x + x2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + 6.5x + 6.25 + x2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + 6.5x + x2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + 6.5x + x2 = 0 + 6.25
6.5x + x2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
6.5x + x2 = 6.25

The x term is 6.5x.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5x + 10.5625 + x2 = 6.25 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = 6.25 + 10.5625

Combine like terms: 6.25 + 10.5625 = 16.8125
10.5625 + 6.5x + x2 = 16.8125

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 16.8125

Calculate the square root of the right side: 4.100304867

Break this problem into two subproblems by setting 
(x + 3.25) equal to 4.100304867 and -4.100304867.

Subproblem 1

x + 3.25 = 4.100304867 Simplifying x + 3.25 = 4.100304867 Reorder the terms: 3.25 + x = 4.100304867 Solving 3.25 + x = 4.100304867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 4.100304867 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 4.100304867 + -3.25 x = 4.100304867 + -3.25 Combine like terms: 4.100304867 + -3.25 = 0.850304867 x = 0.850304867 Simplifying x = 0.850304867

Subproblem 2

x + 3.25 = -4.100304867 Simplifying x + 3.25 = -4.100304867 Reorder the terms: 3.25 + x = -4.100304867 Solving 3.25 + x = -4.100304867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -4.100304867 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -4.100304867 + -3.25 x = -4.100304867 + -3.25 Combine like terms: -4.100304867 + -3.25 = -7.350304867 x = -7.350304867 Simplifying x = -7.350304867

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.850304867, -7.350304867}

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